The Number of Integers Divisible by a^k Except a^(k+l) b

Yanapat Tongron; Kanyaphak Paikhlaew

PDF

Published: Sep 28, 2022

Keywords:

Bounds Ceiling function Divisibility Floor function Integer

Yanapat Tongron

Mathematics and Applied Statistics Program, Faculty of Science and Technology, Nakhon Ratchasima Rajabhat University, Nakhon Ratchasima 30000, Thailand

Kanyaphak Paikhlaew

Mathematics and Applied Statistics Program, Faculty of Science and Technology, Nakhon Ratchasima Rajabhat University, Nakhon Ratchasima 30000, Thailand

Abstract

For positive integers $gif.latex?a,b,k,l,n$ , let $gif.latex?A_{(k,l)}^{(a,b)}(n)$ be the set of all integers divisible by $gif.latex?a^{k}$ except $gif.latex?a^{k+l}b$ between $gif.latex?1$ and $gif.latex?n$ . Under certain condition on these integers, we obtain the explicit formula for $gif.latex?\left&space;|A_{(k,l)}^{(a,b)}(n)&space;\right&space;|$ , where $gif.latex?\left&space;|X&space;\right&space;|$ denotes the number of elements in a finite set $gif.latex?X$ . We also provide bounds on $gif.latex?\left&space;|A_{(k,l)}^{(a,b)}(n)&space;\right&space;|$ and show that these are the best bounds by examples.

How to Cite

Tongron , Y., & Paikhlaew, K. (2022). The Number of Integers Divisible by a^k Except a^(k+l) b. Science & Technology Asia, 27(3), 132–136. retrieved from https://ph02.tci-thaijo.org/index.php/SciTechAsia/article/view/242455

Issue

Vol.27 No.3 (July-September 2022)

Section

Physical sciences

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Article Sidebar

Main Article Content

Abstract

Article Details